Question

Please help me solve this correctly. Show all work. Thanks!

Saturated steam at a gauge pressure of 5.00 bar is to be used to heat a stream of ethane.

The ethane enters a heat exchanger at 16°C and 1.5 bar gauge pressure at a rate of 795 m³/min and is heated at constant pressure to 93°C.

The steam condenses and leaves the exchanger as a liquid at 27.0°C.

Please help solve this correctly. Please show work. Thanks!

The specific enthalpy of ethane at the given pressure is 941 kJ/kg at 16°C and 1073 kJ/kg at 93°C.

You may take the compressibility factor for ethane to be 0.970 at the inlet conditions.

a) How much power in kW must be transferred to the ethane to heat it from 16°C to 93°C?

b) At what rate (m³/s) must steam be supplied to the heat exchanger if all the energy transferred from the steam goes to heat the ethane?

Answer 1

Stream pressure = 5 bar. rightarrow (h_1) rightarrow Enthalpy of steam at(inlet) = hg at 5 bar Tsat at 5 bar = 151.8 degree c. Enthalpy of steam at exit(h_2) = h_f-C_w[T_sat-T] = 640.1-4.187[151.8-27] = 117.5624 KJ/kg Inlet enthalpy of ethane(h_3) = 941 KJ/kg at 16 degree c Exit enthalpy of ethane(h_4) = 1073 KJ/kg at 93 degree c h_f = 640.1 KJ/kg T_sat = 151.8 degree c T = 27 degree c C_w = 4.187 KJ/kg k degree Q(Discharge) of ethane = 795 m^3/min Compressibility factor for ethane z = PV/RT = 0.97 Heat lost by water = Heat taken by ethane. M_s times (h_1-h_2) = m_ethane times (h_4-h_3). M_s times (2748-117.5624) = T_ethane times 795/60[1073-941] rho_ethane = P/RT = 0.970 m_s times 2630.4376 = 0.97 times 795/60 times 132 mass flow rated steam(m's) = 0.64496 kg/s \r\n a) Power in KW given to ethane = m'_ethane[h_4-h_3] = I_ethane times Q'_ethane times [h_4-h_3] = 0.97 times 795/60 times (1073-941] = 1696.53 KW